How far from the grating a screen for the second order minima to occur 6.8cm from the central maxima

erwachsenc6 2022-10-15 Answered
A grating with 1500 lines/cm has blue light with a wavelength of 490 nm incident on it. a. You measure a diffraction angle of 12.7 to one of the maxima. Which order bright spot is this? b. How far from the grating should you place a screen in order for the second order minima (dark spot) to occur 6.8 cm from the central maxima?
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Answers (1)

na1p1a2pafr
Answered 2022-10-16 Author has 16 answers
The equation for diffraction of light is
d sin θ = m λ
where d is the slit width
m is the order of diffraction
tan θ = distance of second minima from central maxima distance of screen from grating = y D
The angle of diffraction is 12.7 degree, wavelength is 490 nm. There are 1500 lines / cm. The slit width is
d = 1 1500   c m = 6.66 × 10 4   c m = 6.66 × 10 6 m
therefore from equation
m = 6.66 × 10 6 sin 12.7 490 × 10 9
diffraction angle for order 2 minima is
sin θ = 2 × 490 × 10 9 6.66 × 10 6 θ = 8.45  degrees
Now from equation , distance of screen is
D = y tan 8.45 = 6.8 0.418   c m
Answer:
a) Order is 3
b) distance of screen from grating is 45.9 cm
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